Math 4980: Mathematical Modeling

     


  • Syllabus


  • Some Matlab files for the homework


  • Homework

    • NOTE: We will have a grader for the class. Therefore, we will collect the homework every Tuesday but no quizzes.

    1/17(T), DUE (T 1/24): 1.1, #1(b,c), 2(b,c), 3(b,c), 4(b,c), 8, 9.

    1/19(Th), DUE (T 1/24): 1.2, #1, 3, 8 and 1.3, #1(a,c,e), 2(a,b,c,i,j), 3(a,b,), 5, 6.

    1/24(T), DUE (T 1/31): 1.4, #1 (a) Please replace the coefficients 0.6, 0.3, 0.4, and 0.7 in Example 1 by 0.1, 0.2, 0.9, and 0.8.
    (b) Please run the experiments using the starting values (1000, 6000) and (6000, 1000).

    1/26(Th), DUE (T 1/31): 1.4, #2 (a) Please replace the coefficients 1.2, 0.001, 1.3, and 0.002 in Example 3
    by 1.1, 0.001, 1.3, and 0.002. (b) Please run the experiments using the starting value (150, 201).
    2.1, #4, 6, 14, 15.

    1/31(T), DUE (T 2/7): 2.2, #1, 2, 3, 7, 9 and 2.3, #2, 4.
    Group Project DUE (T 2/14): Page 89, #3. Construct a model from the data given. Then check your model by comparing
    the predictions by the model with the observations (data).

    2/2(Th), DUE (T 2/7): 3.1, #2, 4(a,b) and 3.2 #1.

    2/7(T), DUE (T 2/14): 3.3, #1, 2(a,b), 4.

    2/9(Th), DUE (T 2/14): 3.4, #2, 5.

    2/14(T), DUE (T 2/21): 4.1, #7, 8 and 4.2, #3 (use the first three data points to find an interpolation polynomial of degree 2
    in Lagrange form).

    2/16(Th), DUE (T 2/21): 4.3, #2, 3, 4, 6 and 4.4, #1(a,b,c) - just find the piecewise linear (order 1) spline.

    2/21(T), DUE (T 2/28): 5.1, #3, 4, 5, 6.

    2/23(Th), DUE (T 2/28): 5.2, #1(a,b,d), 2(b,c,d) and 5.3, #1, 2, 3, 5.

    3/1(Th), DUE (T 3/6): 5.4, #3. First build the linear spline model using the cumulative probability and use Monte Carlo to
    simulate the number of occurences. Then find the inverse linear spline and simulate the lag time of a random day.

    3/6(T), DUE (T 3/13): 5.5, #1.

    3/8(Th), DUE (T 3/13): 6.1, #1, 2 and 6.2, #1, 2, 3.

    3/13(T), DUE (T 3/27): 6.3, #1, 2, and predict weight as a function of the square of height, i.e., let y=w and x=h^2.
    Group Project DUE (T 4/3): Page 213, #4(a). Follow the steps we outlined in class. For (III), narrow the search for the
    best value of S to an interval of length 50 and make runs of 5000 simulations for each of ten equally spaced values of S.
    Then finally narrow the search for the best value of S to an interval of length 20 and make runs of 10,000 simulations for
    each of twenty equally spaced values of S. Now you have the answer for the best value of S, i.e., the best pool size.
    Please also give the lowest expected cost to the school district.

    3/15(Th), DUE (T 3/27): 7.1, #1, 2.

    3/27(T), DUE (T 4/3): 7.2, #1, 2, 6, 11.

    3/29(Th), DUE (T 4/3): 7.3, #1, 5, 8(a,b) and 7.5, #1, 2.

    4/3(T), DUE (T 4/10): 8.1, #1, 2, 6 and 8.2, #1, 2, 3.

    4/5(Th), DUE (T 4/10): 8.3, #10, 12 and 8.4, #1.

    4/10(T), DUE (Th 4/19): 8.4, #3.

    4/12(Th), DUE (Th 4/19): 10.2, #1, 2.
    Hint: to graph the result, set x(1)=0, y(1)=0, calculate x(k) and y(k) for k=1,2,...,20.
    Then plot (x(k),y(k+1)) and plot (x(k+1),y(k)) for all k.

    4/19(Th), DUE (T 4/24): 11.1, #1, 3, 4.

    4/24(T), DUE (T 5/1): 11.2, #1, 2, 3, 4, 5.

    4/26(Th), DUE (T 5/1): 11.4, #1, 2, 3, 4.
    Group Project DUE (Th 5/10): Modules in Undergraduate Mathametics and Its Applications, Module 73, Epdemics:
    Applications of Calculus to Medicine. Please read the module and finish Exercises #1, 2, 3, 4.



  • Announcement

  • The first exam will be on Tuesday 2/28 which will cover the following sections: 1.1, 1.2, 1.3, 1.4, 2.1, 2.2, 2.3, 3.1,
    3.2, 3.3, 3.4, 4.1, 4.2, 4.3, and 4.4.

  • The second exam will be on Tuesday 4/17 which will cover the following sections: 5.1, 5.2, 5.3, 5.4, 5.5, 6.1, 6.2, 6.3,
    7.1, 7.2, 7.3, 7.5, 8.1, 8.2, 8.3, and 8.4.

  • The final exam will be on Thursday 5/10 at 10:30AM. The final will be comprehensive. In addition to the sections in the
    midterms, the following sections will be covered: 10.2, 11.1, 11.2, 11.4.







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